Welcome to Aerospace Engineering DESIGN-CENTERED INTRODUCTION TO AEROSPACE ENGINEERING Notes 4 Topics 1. Course Organization 2. Today's Dreams in Various Speed Ranges 3. Designing a Flight Vehicle: Route Map of Disciplines 4. Mission Specification & Take Off Weight 5. Force Balance during flight 6. Earth's Atmosphere 7. Aerodynamics 8. Propulsion 9.Performance, Stability & Control 10. Structures and Materials 11. High Speed Flight 12. Space Flight
AERODYNAMICS http://www.andes.org.uk/andes-information-files/condor-puna-2005.jpg
AERODYNAMICS LIFT AND DRAG Aerodynamic Lift is the force perpendicular to the freestream. It is generated by deflecting the freestream air. According to Newton s 1 st & 3 rd laws, lift is the reaction to the rate of change of momentum of air, perpendicular to the freestream. Drag is force along the freestream direction acting on the vehicle. It is due to irreversible loss of momentum.
Lift is related to freestream velocity by C L Lift and Drag U SC L is the lift coefficient, and S is the planform area of the wing. L 2 2 where The drag is given by: D U 2 2 SC D Lift to Drag Ratio L / D C C L C D We want our airplanes to have as high L/D as possible!
In low-speed flows of air (<0.3 times the speed of sound, or Mach 0.3), there are 3 main ways of creating aerodynamic lift: All involve directing the momentum perpendicular to the freestream. 1. Vary the Angle of Attack 2. Camber 3. Vortex-induced lift
In each case shown above, the flow moves more rapidly at some places than at others. In these regions of high velocity, the pressure is lower. The relation between pressure and velocity in low- speed flow is given by the Bernoulli equation:, or 1 p 0 p U 2 This equation is derived from Newton's Second Law of Motion, which expresses "Conservation of Momentum". p 0 is called the Stagnation pressure, or total pressure. P is called the Static pressure. 1 2 is called the dynamic pressure, also denoted as "q". 2 U 2
Pressure Coefficient The pressure coefficient is a way to express the pressure with respect to some reference pressure, as a "dimensionless" quantity. Cp = 0 indicates the undisturbed freestream value of static pressure. Cp = 1 indicates a stagnation point. Cp < 0 indicates a suction region Chordwise pressure distribution over an airfoil in low-speed flow
Exercise: Pressure Coefficient What is the pressure coefficient at the stagnation point of an airfoil section? What is the pressure coefficient on a flat surface aligned with the freestream? Cp at the suction peak of an airfoil is -1.2. What is the pressure there as a percentage of the freestream dynamic pressure? What is the velocity at this point, as a percentage of the freestream velocity?
Airfoil (British: aerofoil ) Airfoil means shape of a section of a wing. It is a two-dimensional concept. Airfoils cannot fly: wings fly. Airfoil properties are used to calculate and design wing properties. Airfoil lift coefficient varies with angle of attack If the airfoil il is cambered, the lift coefficient i is positive even at zero angle of attack, and reaches zero only at some negative value of angle of atack: this is called the "zero-lift angle of attack", As the camber is increased, becomes more negative. Thus airfoil lift coefficient is The lift-curve slope is,where is in radians.
Exercise:Lift coefficient The angle of attack of an airfoil is 12 degrees. The lift curve slope is 5.8 per radian. Zero-lift angle of attack is -2 degrees. Find the lift coefficient. If the air density is 1/10 of sea-level standard, and the temperature is 20 deg. C higher than the standard sea-level, flight speed is 100 m/s and wing planform area is 30m^2, find the lift.
LIFT-INDUCED DRAG and ASPECT RATIO At the ends of the wings, the pressure difference between the upper and lower sides is lost, as the flow rolls up into a vortex. The Aspect Ratio of a wing is defined as: AR 2 b S where b is the wing span and S is the wing planform area.
Effects of Finite Aspect Ratio 1. The overall lift is reduced, relative to the airfoil lift value predicted for a section of an infinite wing. 2. The lift vector is tilted back, so that an "induced drag" is created. Both of these (usually undesirable) effects are reduced by increasing the Aspect Ratio Both of these (usually undesirable) effects are reduced by increasing the Aspect Ratio of the wing.
Drag Coefficient The drag is given by: The drag coefficient in low-speed flow is composed of 3 parts: where is the parasite drag, which is independent of lift. It is usually due to the losses of stagnation p g, p y g pressure which occur when part of the flow separates somewhere along the wing or body surface. In high speed flight, the effect of shocks and wave drag must be added to this, and becomes the dominant source of drag.
Most aircraft are designed to minimize The profile drag of an airfoil of chord 1unit is about the same as that of a circular cylinder whose diameter is only 0.005 units.
is the skin friction drag, which is due to viscosity. is the Induced Drag. In low-speed flight, this is the largest cause of drag, because you have to have lift to fly, and this drag is caused by lift. Here e is called the "spanwise efficiency factor". It is the answer to the question: How does this wing rate compared to the ideal wing for this aspect ratio? Its value is usually close to 1, perhaps as high h as 0.99. Note that: so that. Also, as To minimize induced drag, one should design wings with the largest possible aspect ratio, but also provide enough surface area so that you need only a small angle of attack to provide the necessary lift even at low speed
Example: of a small airliner is 0.018. Wing aspect ratio is 6. Assume spanwise efficiency is 0.9. Lift coefficient is 0.5. Find the total drag coefficient. If the density is 1 kg/m3 and speed is 200m/s, find the drag.
http://www.andes.org.uk/andes-information- files/condor-puna-2005.jpg
Vortex-Induced Lift and Delta Wings
Speed for Minimum Drag Total drag is composed of a part which depends on lift, and one that does not. Let us consider what it takes to keep L = W So. i.e, Or, Minimum Total Drag = twice zero lift drag.. This is a remarkable result: It means that: AIRCRAFT, UNLIKE OTHER FORMS OF TRANSPORTATION, HAVE A DEFINITE SPEED FOR MINIMUM DRAG!
To fly an airplane of a given weight, straight and level, the condition for minimum drag (maximum lift-to-drag ratio) is that the profile drag coefficient is the same as the induced drag coefficient.
Example An aircraft has a wing loading (W/S) of 130 pounds per square foot (6233N/m2), aspect ratio of 7.667, and wing span of 60.96m. We'll assume that its spanwise efficiency factor will be 0.99. Let's assume that the profile drag coefficient is given by Thus, for maximum Lift-to-Drag ratio (minimum drag, and the lift is always equal to the weight for straight and level flight), The corresponding C L is calculated as 0.598, and the dynamic pressure is 10423N/m 2. At 11,000 meters in the Standard Atmosphere, density is 0.36kg/m 3, so that the flight speed is 240.64 m/s. Note: In practice, the CD 0 might change with flight Mach number, for high-speed flight. This is not taken into account in the above.
AERODYNAMICS SUMMARY Lift is force perpendicular to the flow direction, due to pressure differences across surfaces. 3 ways of generating lift: a) angle of attack b) camber c) vortex-induced lift. An infinite (2-dimensional) wing is entirely described by its airfoil section. Finite wings have less lift than corresponding span-lengths of an infinite wing at the same angle of attack, and also have lift-induced drag. The total drag is composed of profile drag, which does not vary with lift, and induced drag, which rises as the square of the lift coefficient. To fly an airplane of a given weight, straight and level, the condition for minimum drag (maximum lift-to-drag ratio) is that the profile drag coefficient i is the same as the induced d drag coefficient.
WING LOADING AND CRUISE DESIGN POINT The wing loading,, is a decision i to be made by the designer. If W/S is low, then the aircraft will be efficient in low-speed flight, and perhaps have lower aerodynamic noise in high h speed flight, but the structure t may weigh too much (large wings) and the skin friction drag will be high in high-speed flight. Also, the aircraft will be more responsive to gusts, and hence will get bounced around a lot. Low wing loading is good for gliders and for aircraft intended for long endurance. The wing loading goes up as the expected design speed goes up. For a transonic airliner, a typical wing loading value is around 120 to 140 psf.
Design Step 4 10. Select cruise wing loading find wing area 11. Select wing span find aspect ratio 12. Find cruise lift coefficient 13. Guess achievable zero-lift drag coefficient. Find induced drag coefft;, total L/D 14. Find speed for minimum drag